I would go with answer choice J.
We are given the function <span>x^2+8x+4y+4=0. To determine the characteristics of this function, we need to write it in the standard form as follows:
</span><span>x^2+8x+4y+4=0
4y = -x^2 - 8x - 4
y = (-1/4)x^2 - 2x - 1
To determine the vertex and the focus of the parabola, we write it in the form </span>(y+k)^2 = x+h by completing the square method.
y + 1 = (-1/4)x^2 - 2x
y +1 = (-1/4)(x^2 + x/2)
y +1 - 1/64 = (-1/4)(x^2 + x/2 + 1/16)
y + 15/16 = (-1/4) (x + 1/4)^2
The vertex would be at point ( -1/4, -15/16)
The focus would be determined as follows:
<span>4p=-1/4 so p=-1/8
focus = (-1/4+(-1/8),-15/16) = (-3/8,-15/16)
Directrix = </span><span>x = h - p
x = -1/4 - -1/8 = -1/8 </span>
Answer: 
Step-by-step explanation:
In a fraction, you can cancel factorials if they are present in the numerator and denominator
To find the point of intersection, we want to set the two equations equal to each other to find where they meet. The problem is, we have two variables, which means we can't just set them equal to each other as is. We need to manipulate the equations so that we can remove one of the variables at a time to solve for the other one.
First, let's move y to one side so we can solve for x.
2x-3y=9
2x-9=3y
y=(2x-9)/3
5x+4y=11
4y=11-5x
y=(11-5x)/4
Now that they both equal the same thing (y), we can set them equal to each other and solve for x. This will give us the x value for the point of intersection of the lines.
(11-5x)/4=(2x-9)/3
3(11-5x)=4(2x-9)
33-15x=8x-36
33+36=8x+15x
69=23x
x=69/23
x=3
Now, we can do the opposite, and solve for x to find the y coordinate.
2x-3y=9
2x=3y+9
x=(3y+9)/2
5x+4y=11
5x=11-4y
x=(11-4y)/5
(3y+9)/2=(11-4y)/5
5(3y+9)=2(11-4y)
15y+45=22-8y
15y+8y=22-45
23y= -23
y= -1
The coordinates for the point of intersection of the two lines is (3, -1).
